A circuit has four inputs and two outputs. The inputs A$3$:$0$ represent a number from $0$

to $15.$ Output $P$ should be TRUE if the number is prime $(0$ and $1$ are not prime, but

$2,3,5$ and so on are prime$).$ Output D should be TRUE if the number is divisible by $3.$

$($hint: $0$ is not divisible by $3).$ Write Sums of Products $($SOP$)$ representation for P and D $.$

$P-A_{95}{A}_2{A}_1{A}_0+A_3^{\text{'}}{A}_2{A}_1^{\text{'}}{A}_0$

$D=A_3{A}_9{A}_1{A}_0+A_3{A}_7{A}_1^{\text{'}}{A}_0^{\text{'}}$

$P=A_3{A}_9{A}_1{A}_0+A_3^{\text{'}}{A}_3{A}_1{A}_0$

$D=A_1{A}_2{A}_1{A}_0+A_0{A}_2{A}_1^{\text{'}}{A}_0^{\text{'}}$

Nonc of them

$P=A_3{A}_9{A}_1{A}_0+A_3^{\text{'}}{A}_3{A}_1{A}_0$

$D-A_3{A}_2{A}_1{A}_0+A_3{A}_2^{\text{'}}{A}_1^{\text{'}}{A}_0^{\text{'}}$

$P=A_3{A}_2{A}_1{A}_0+A_1^{\text{'}}{A}_2^{\text{'}}{A}_1^{\text{'}}{A}_0$

$D=A_3{A}_9{A}_1{A}_0+A_3{A}_3^{\text{'}}{A}_1^{\text{'}}{A}_{11}^{\text{'}}$